Previous article Next article Full AccessA Note on Estimating the Optimal Regularization ParameterJohn W. HilgersJohn W. Hilgershttps://doi.org/10.1137/0717040PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe behavior of a quantity which in some cases permits the approximation of the optimal regularization parameter is examined. A previously considered numerical example is shown to conform to theory.[1] J. W. Hilgers, Noniterative methods for solving operator equations of the first kind, MRC Tech. Summ. Rep., 1413, Mathematics Research Center, University of Wisconsin, Madison WI, 1973 Google Scholar[2] J. W. Hilgers, Approximating the optimal regularization parameter, MRC Tech. Summ. Rep., 1472, Mathematics Research Center, University of Wisconsin, Madison WI, 1974 Google Scholar[3] John W. Hilgers, On the equivalence of regularization and certain reproducing kernel Hilbert space approaches for solving first kind problems, SIAM J. Numer. Anal., 13 (1976), 172–184 10.1137/0713018 57:11030 0324.47008 LinkISIGoogle Scholar[4] J. W. Hilgers, Erratum: “On the equivalence of regularization and certain reproducing kernel Hilbert space approaches for solving first kind problems”, SIAM J. Numer. Anal., 15 (1978), 1301– 10.1137/0715089 80a:65268 0395.65027 LinkISIGoogle Scholar[5] M. Z. Nashed and , Grace Wahba, Generalized inverses in reproducing kernel spaces: an approach to regularization of linear operator equations, SIAM J. Math. Anal., 5 (1974), 974–987 10.1137/0505095 50:10871 0287.47009 LinkISIGoogle Scholar[6] F. Smithies, Integral equations, Cambridge University Press, Cambridge, 1970 Google Scholar[7] J. M. Varah, A practical examination of some numerical methods for linear discrete ill-posed problems, SIAM Rev., 21 (1979), 100–111 10.1137/1021007 80c:65075 0406.65015 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Bayesian approach to introducing anatomo-functional priors in the EEG/MEG inverse problemIEEE Transactions on Biomedical Engineering, Vol. 44, No. 5 Cross Ref Image reconstruction and restoration: overview of common estimation structures and problemsIEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 37, No. 12 Cross Ref Volume 17, Issue 3| 1980SIAM Journal on Numerical Analysis History Submitted:09 May 1979Published online:17 July 2006 InformationCopyright © 1980 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0717040Article page range:pp. 472-473ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics